On the mechanical behavior of the human biliary system

Abstract

This paper reviews the progress made in understanding the mechanical behaviour of the biliary system. Gallstones and diseases of the biliary tract affect more than 10% of the adult population. The complications of gallstones, i.e. acute pancreatitis and obstructive jandice, can be lethal, and patients with acalculous gallbladder pain often pose diagnostic difficulties and undergo repeated ultrasound scans and oral cholecystograms. Moreover, surgery to remove the gallbladder in these patients, in an attempt to relieve the symptoms, gives variable results. Extensive research has been carried out to understand the physiological and pathological functions of the biliary system, but the mechanism of the pathogenesis of gallstones and pain production still remain poorly understood. It is believed that the mechanical factors play an essential role in the mechanisms of the gallstone formation and biliary diseases. However, despite the extensive literature in clinical studies, only limited work has been carried out to study the biliary system from the mechanical point of view. In this paper, we discuss the state of art knowledge of the fluid dynamics of bile flow in the biliary tract, the solid mechanics of the gallbladder and bile ducts, recent mathematical and numerical modelling of the system, and finally the future challenges in the area.

Figure 1

The geometry of the biliary tract, where the valves of Heister in the cystic duct are shown.

Figure 2

Two types of the cystic duct models used by Ooi et al[43] (modified from Figure 2 in the Journal of Biomechanics, vol 37, page 1913-1922) .

Figure 3

Computational models built from two patients' biliary system images used by Ooi et a[[43] (modified from Journal of Biomechanics, vol. 37, page 1913-1922, Figure 2). Patient A is reported to have gallstones, and patient B is the normal control.

Figure 4

The resistance, Rd, plotted with the Reynolds number, Re (which is defined as the ratio of inertia over viscous forces, and is proportional to the flow rate for a given duct and bile). n is the number of the baffles in the duct[43] (modified from Journal of Biomechanics, vol. 37, page 1913-1922, Figure 6).

Figure 5

One-dimensional model of human billiary system and bile flow directions in the (a) emptying and (b) refill phases, (c) details of baffles at one section of the cystic duct[44]. p is the pressure inside the gallbladder, and Q is the flow rate of bile fluid. (Modified from figure 2 to be published in ASME Journal of Biomechanical Engineering).

Figure 6

Pressure loss variations with baffle height ratio (A) and baffle number (B) for both rigid and elastic models[44]. (Modified from figure 8 to be published in ASME Journal of Biomechanical Engineering).

Figure 7

Gallbladder body shape during emptying is assumed to be ellipsoidal with major and minor axis lengths D₁, D₂ and D₃ (D₁ > D₂ ≥ D₃); the gallbladder is subjected to a uniform internal pressure. The stress due to the pressure at any point P has three components, σ_θ (meridian), σ_φ (latitude) and τ_θφ (in surface)[85].

Math 1

Math(A1).

Figure 8

Li et al[85] calculated the stress distributions for two different subjects: R (left) and G (right). The top frame is the principal meridian stress, σ_θ, the middle frame is the principal latitude stress, σ_φ, and the bottom one is the in-plane shear stress τ_θφ. It is seen that the location and the maximum stresses change as the ratio of the lengths of the three axes change.